你的第一个神经网络

在此项目中,你将构建你的第一个神经网络,并用该网络预测每日自行车租客人数。我们提供了一些代码,但是需要你来实现神经网络(大部分内容)。提交此项目后,欢迎进一步探索该数据和模型。

In [1]:
%matplotlib inline
%config InlineBackend.figure_format = 'retina'

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt

加载和准备数据

构建神经网络的关键一步是正确地准备数据。不同尺度级别的变量使网络难以高效地掌握正确的权重。我们在下方已经提供了加载和准备数据的代码。你很快将进一步学习这些代码!

In [2]:
data_path = 'Bike-Sharing-Dataset/hour.csv'

rides = pd.read_csv(data_path)
In [3]:
rides[:100]
Out[3]:
instant dteday season yr mnth hr holiday weekday workingday weathersit temp atemp hum windspeed casual registered cnt
0 1 2011-01-01 1 0 1 0 0 6 0 1 0.24 0.2879 0.81 0.0000 3 13 16
1 2 2011-01-01 1 0 1 1 0 6 0 1 0.22 0.2727 0.80 0.0000 8 32 40
2 3 2011-01-01 1 0 1 2 0 6 0 1 0.22 0.2727 0.80 0.0000 5 27 32
3 4 2011-01-01 1 0 1 3 0 6 0 1 0.24 0.2879 0.75 0.0000 3 10 13
4 5 2011-01-01 1 0 1 4 0 6 0 1 0.24 0.2879 0.75 0.0000 0 1 1
5 6 2011-01-01 1 0 1 5 0 6 0 2 0.24 0.2576 0.75 0.0896 0 1 1
6 7 2011-01-01 1 0 1 6 0 6 0 1 0.22 0.2727 0.80 0.0000 2 0 2
7 8 2011-01-01 1 0 1 7 0 6 0 1 0.20 0.2576 0.86 0.0000 1 2 3
8 9 2011-01-01 1 0 1 8 0 6 0 1 0.24 0.2879 0.75 0.0000 1 7 8
9 10 2011-01-01 1 0 1 9 0 6 0 1 0.32 0.3485 0.76 0.0000 8 6 14
10 11 2011-01-01 1 0 1 10 0 6 0 1 0.38 0.3939 0.76 0.2537 12 24 36
11 12 2011-01-01 1 0 1 11 0 6 0 1 0.36 0.3333 0.81 0.2836 26 30 56
12 13 2011-01-01 1 0 1 12 0 6 0 1 0.42 0.4242 0.77 0.2836 29 55 84
13 14 2011-01-01 1 0 1 13 0 6 0 2 0.46 0.4545 0.72 0.2985 47 47 94
14 15 2011-01-01 1 0 1 14 0 6 0 2 0.46 0.4545 0.72 0.2836 35 71 106
15 16 2011-01-01 1 0 1 15 0 6 0 2 0.44 0.4394 0.77 0.2985 40 70 110
16 17 2011-01-01 1 0 1 16 0 6 0 2 0.42 0.4242 0.82 0.2985 41 52 93
17 18 2011-01-01 1 0 1 17 0 6 0 2 0.44 0.4394 0.82 0.2836 15 52 67
18 19 2011-01-01 1 0 1 18 0 6 0 3 0.42 0.4242 0.88 0.2537 9 26 35
19 20 2011-01-01 1 0 1 19 0 6 0 3 0.42 0.4242 0.88 0.2537 6 31 37
20 21 2011-01-01 1 0 1 20 0 6 0 2 0.40 0.4091 0.87 0.2537 11 25 36
21 22 2011-01-01 1 0 1 21 0 6 0 2 0.40 0.4091 0.87 0.1940 3 31 34
22 23 2011-01-01 1 0 1 22 0 6 0 2 0.40 0.4091 0.94 0.2239 11 17 28
23 24 2011-01-01 1 0 1 23 0 6 0 2 0.46 0.4545 0.88 0.2985 15 24 39
24 25 2011-01-02 1 0 1 0 0 0 0 2 0.46 0.4545 0.88 0.2985 4 13 17
25 26 2011-01-02 1 0 1 1 0 0 0 2 0.44 0.4394 0.94 0.2537 1 16 17
26 27 2011-01-02 1 0 1 2 0 0 0 2 0.42 0.4242 1.00 0.2836 1 8 9
27 28 2011-01-02 1 0 1 3 0 0 0 2 0.46 0.4545 0.94 0.1940 2 4 6
28 29 2011-01-02 1 0 1 4 0 0 0 2 0.46 0.4545 0.94 0.1940 2 1 3
29 30 2011-01-02 1 0 1 6 0 0 0 3 0.42 0.4242 0.77 0.2985 0 2 2
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
70 71 2011-01-04 1 0 1 1 0 2 1 1 0.16 0.1818 0.59 0.1045 0 2 2
71 72 2011-01-04 1 0 1 2 0 2 1 1 0.14 0.1515 0.63 0.1343 0 1 1
72 73 2011-01-04 1 0 1 4 0 2 1 1 0.14 0.1818 0.63 0.0896 0 2 2
73 74 2011-01-04 1 0 1 5 0 2 1 1 0.12 0.1515 0.68 0.1045 0 4 4
74 75 2011-01-04 1 0 1 6 0 2 1 1 0.12 0.1515 0.74 0.1045 0 36 36
75 76 2011-01-04 1 0 1 7 0 2 1 1 0.12 0.1515 0.74 0.1343 2 92 94
76 77 2011-01-04 1 0 1 8 0 2 1 1 0.14 0.1515 0.69 0.1642 2 177 179
77 78 2011-01-04 1 0 1 9 0 2 1 1 0.16 0.1515 0.64 0.2239 2 98 100
78 79 2011-01-04 1 0 1 10 0 2 1 2 0.16 0.1364 0.69 0.3284 5 37 42
79 80 2011-01-04 1 0 1 11 0 2 1 1 0.22 0.2121 0.51 0.2985 7 50 57
80 81 2011-01-04 1 0 1 12 0 2 1 1 0.22 0.2273 0.51 0.1642 12 66 78
81 82 2011-01-04 1 0 1 13 0 2 1 1 0.24 0.2273 0.56 0.1940 18 79 97
82 83 2011-01-04 1 0 1 14 0 2 1 1 0.26 0.2576 0.52 0.2239 9 54 63
83 84 2011-01-04 1 0 1 15 0 2 1 1 0.28 0.2727 0.52 0.2537 17 48 65
84 85 2011-01-04 1 0 1 16 0 2 1 1 0.30 0.2879 0.49 0.2537 15 68 83
85 86 2011-01-04 1 0 1 17 0 2 1 1 0.28 0.2727 0.48 0.2239 10 202 212
86 87 2011-01-04 1 0 1 18 0 2 1 1 0.26 0.2576 0.48 0.1940 3 179 182
87 88 2011-01-04 1 0 1 19 0 2 1 1 0.24 0.2576 0.48 0.1045 2 110 112
88 89 2011-01-04 1 0 1 20 0 2 1 1 0.24 0.2576 0.48 0.1045 1 53 54
89 90 2011-01-04 1 0 1 21 0 2 1 1 0.22 0.2727 0.64 0.0000 0 48 48
90 91 2011-01-04 1 0 1 22 0 2 1 1 0.22 0.2576 0.64 0.0896 1 34 35
91 92 2011-01-04 1 0 1 23 0 2 1 1 0.20 0.2273 0.69 0.0896 2 9 11
92 93 2011-01-05 1 0 1 0 0 3 1 1 0.20 0.2576 0.64 0.0000 0 6 6
93 94 2011-01-05 1 0 1 1 0 3 1 1 0.16 0.1970 0.74 0.0896 0 6 6
94 95 2011-01-05 1 0 1 2 0 3 1 1 0.16 0.1970 0.74 0.0896 0 2 2
95 96 2011-01-05 1 0 1 4 0 3 1 1 0.24 0.2273 0.48 0.2239 0 2 2
96 97 2011-01-05 1 0 1 5 0 3 1 1 0.22 0.2273 0.47 0.1642 0 3 3
97 98 2011-01-05 1 0 1 6 0 3 1 1 0.20 0.1970 0.47 0.2239 0 33 33
98 99 2011-01-05 1 0 1 7 0 3 1 1 0.18 0.1818 0.43 0.1940 1 87 88
99 100 2011-01-05 1 0 1 8 0 3 1 1 0.20 0.1818 0.40 0.2985 3 192 195

100 rows × 17 columns

数据简介

此数据集包含的是从 2011 年 1 月 1 日到 2012 年 12 月 31 日期间每天每小时的骑车人数。骑车用户分成临时用户和注册用户,cnt 列是骑车用户数汇总列。你可以在上方看到前几行数据。

下图展示的是数据集中前 10 天左右的骑车人数(某些天不一定是 24 个条目,所以不是精确的 10 天)。你可以在这里看到每小时租金。这些数据很复杂!周末的骑行人数少些,工作日上下班期间是骑行高峰期。我们还可以从上方的数据中看到温度、湿度和风速信息,所有这些信息都会影响骑行人数。你需要用你的模型展示所有这些数据。

In [4]:
rides[:24*10].plot(x='dteday', y='cnt')
Out[4]:
<matplotlib.axes._subplots.AxesSubplot at 0x7f4bb0323f60>

虚拟变量(哑变量)

下面是一些分类变量,例如季节、天气、月份。要在我们的模型中包含这些数据,我们需要创建二进制虚拟变量。用 Pandas 库中的 get_dummies() 就可以轻松实现。

In [5]:
dummy_fields = ['season', 'weathersit', 'mnth', 'hr', 'weekday']
for each in dummy_fields:
    dummies = pd.get_dummies(rides[each], prefix=each, drop_first=False)
    rides = pd.concat([rides, dummies], axis=1)

fields_to_drop = ['instant', 'dteday', 'season', 'weathersit', 
                  'weekday', 'atemp', 'mnth', 'workingday', 'hr']
data = rides.drop(fields_to_drop, axis=1)
data.head()
Out[5]:
yr holiday temp hum windspeed casual registered cnt season_1 season_2 ... hr_21 hr_22 hr_23 weekday_0 weekday_1 weekday_2 weekday_3 weekday_4 weekday_5 weekday_6
0 0 0 0.24 0.81 0.0 3 13 16 1 0 ... 0 0 0 0 0 0 0 0 0 1
1 0 0 0.22 0.80 0.0 8 32 40 1 0 ... 0 0 0 0 0 0 0 0 0 1
2 0 0 0.22 0.80 0.0 5 27 32 1 0 ... 0 0 0 0 0 0 0 0 0 1
3 0 0 0.24 0.75 0.0 3 10 13 1 0 ... 0 0 0 0 0 0 0 0 0 1
4 0 0 0.24 0.75 0.0 0 1 1 1 0 ... 0 0 0 0 0 0 0 0 0 1

5 rows × 59 columns

调整目标变量

为了更轻松地训练网络,我们将对每个连续变量标准化,即转换和调整变量,使它们的均值为 0,标准差为 1。

我们会保存换算因子,以便当我们使用网络进行预测时可以还原数据。

In [6]:
quant_features = ['casual', 'registered', 'cnt', 'temp', 'hum', 'windspeed']
# Store scalings in a dictionary so we can convert back later
scaled_features = {}
for each in quant_features:
    mean, std = data[each].mean(), data[each].std()
    scaled_features[each] = [mean, std]
    data.loc[:, each] = (data[each] - mean)/std

将数据拆分为训练、测试和验证数据集

我们将大约最后 21 天的数据保存为测试数据集,这些数据集会在训练完网络后使用。我们将使用该数据集进行预测,并与实际的骑行人数进行对比。

In [7]:
# Save data for approximately the last 21 days 
test_data = data[-21*24:]

# Now remove the test data from the data set 
data = data[:-21*24]

# Separate the data into features and targets
target_fields = ['cnt', 'casual', 'registered']
features, targets = data.drop(target_fields, axis=1), data[target_fields]
test_features, test_targets = test_data.drop(target_fields, axis=1), test_data[target_fields]

我们将数据拆分为两个数据集,一个用作训练,一个在网络训练完后用来验证网络。因为数据是有时间序列特性的,所以我们用历史数据进行训练,然后尝试预测未来数据(验证数据集)。

In [8]:
# Hold out the last 60 days or so of the remaining data as a validation set
train_features, train_targets = features[:-60*24], targets[:-60*24]
val_features, val_targets = features[-60*24:], targets[-60*24:]

开始构建网络

下面你将构建自己的网络。我们已经构建好结构和反向传递部分。你将实现网络的前向传递部分。还需要设置超参数:学习速率、隐藏单元的数量,以及训练传递数量。

该网络有两个层级,一个隐藏层和一个输出层。隐藏层级将使用 S 型函数作为激活函数。输出层只有一个节点,用于递归,节点的输出和节点的输入相同。即激活函数是 $f(x)=x$。这种函数获得输入信号,并生成输出信号,但是会考虑阈值,称为激活函数。我们完成网络的每个层级,并计算每个神经元的输出。一个层级的所有输出变成下一层级神经元的输入。这一流程叫做前向传播(forward propagation)。

我们在神经网络中使用权重将信号从输入层传播到输出层。我们还使用权重将错误从输出层传播回网络,以便更新权重。这叫做反向传播(backpropagation)。

提示:你需要为反向传播实现计算输出激活函数 ($f(x) = x$) 的导数。如果你不熟悉微积分,其实该函数就等同于等式 $y = x$。该等式的斜率是多少?也就是导数 $f(x)$。

你需要完成以下任务:

  1. 实现 S 型激活函数。将 __init__ 中的 self.activation_function 设为你的 S 型函数。
  2. train 方法中实现前向传递。
  3. train 方法中实现反向传播算法,包括计算输出错误。
  4. run 方法中实现前向传递。
In [9]:
class NeuralNetwork(object):
    def __init__(self, input_nodes, hidden_nodes, output_nodes, learning_rate):
        # Set number of nodes in input, hidden and output layers.
        self.input_nodes = input_nodes
        
        self.hidden_nodes = hidden_nodes
        self.output_nodes = output_nodes

        # Initialize weights
        self.weights_input_to_hidden = np.random.normal(0.0, self.input_nodes**-0.5, 
                                       (self.input_nodes, self.hidden_nodes))
        #print("self.weights_input_to_hidden",self.weights_input_to_hidden.shape)
        self.weights_hidden_to_output = np.random.normal(0.0, self.hidden_nodes**-0.5, 
                                       (self.hidden_nodes, self.output_nodes))
        self.lr = learning_rate
        print("self.weights_hidden_to_output ",self.weights_hidden_to_output.shape )
       #### TODO: Set self.activation_function to your implemented sigmoid function ####
        #
        # Note: in Python, you can define a function with a lambda expression,
        # as shown below.
        self.activation_function = lambda x : 1 / ( 1 + np.exp(-x) ) # Replace 0 with your sigmoid calculation.
        
        ### If the lambda code above is not something you're familiar with,
        # You can uncomment out the following three lines and put your 
        # implementation there instead.
        #
        #def sigmoid(x):
         #   return 1/1+np.exp(-x)  # Replace 0 with your sigmoid calculation here
        #self.activation_function = sigmoid
                    
    
        
    def train(self, features, targets):
        ''' Train the network on batch of features and targets. 
        
            Arguments
            ---------
            
            features: 2D array, each row is one data record, each column is a feature
            targets: 1D array of target values
        
        '''
        n_records = features.shape[0]
        delta_weights_i_h = np.zeros(self.weights_input_to_hidden.shape)
        delta_weights_h_o = np.zeros(self.weights_hidden_to_output.shape)
        for X, y in zip(features, targets):
            print("X",X)
            #### Implement the forward pass here ####
            ### Forward pass ###
            # TODO: Hidden layer - Replace these values with your calculations.
            hidden_inputs =np.dot(X,self.weights_input_to_hidden)
            print("hidden_inputs",hidden_inputs)
            
            hidden_outputs = self.activation_function( hidden_inputs ) # signals from hidden layer
            print("hidden_outputs",hidden_outputs)
            # TODO: Output layer - Replace these values with your calculations.
            final_inputs =np.dot(hidden_outputs,self.weights_hidden_to_output)# signals into final output layer
            final_outputs = final_inputs # signals from final output layer
            
            #### Implement the backward pass here ####
            
            ### Backward pass ###

            # TODO: Output error - Replace this value with your calculations.
            error = y-final_outputs # Output layer error is the difference between desired target and actual output.
            print("error",error)
            output_error_term = error
            # TODO: Calculate the hidden layer's contribution to the error
            hidden_error =np.dot(self.weights_hidden_to_output,output_error_term)
            print("hidden_error",hidden_error)
            # TODO: Backpropagated error terms - Replace these values with your calculations.
            
            hidden_error_term = hidden_error*(hidden_outputs*(1-hidden_outputs))
            print("hidden_outputs*(1-hidden_outputs)",(hidden_outputs*(1-hidden_outputs)))
            # Weight step (input to hidden)
            print("hidden_error_term",hidden_error_term)
            print("X=",X)
            delta_weights_i_h +=hidden_error_term*X[:,None]
            
            # Weight step (hidden to output)
            
            delta_weights_h_o += output_error_term*hidden_outputs[:,None]

        # TODO: Update the weights - Replace these values with your calculations.
        self.weights_hidden_to_output += self.lr *delta_weights_h_o/n_records# update hidden-to-output weights with gradient descent step
        self.weights_input_to_hidden += self.lr*delta_weights_i_h/n_records # update input-to-hidden weights with gradient descent step
 
    def run(self, features):
        ''' Run a forward pass through the network with input features 
        
            Arguments
            ---------
            features: 1D array of feature values
        '''
        
        #### Implement the forward pass here ####
        # TODO: Hidden layer - replace these values with the appropriate calculations.
        hidden_inputs =np.dot(features,self.weights_input_to_hidden)  # signals into hidden layer
        hidden_outputs = self.activation_function( hidden_inputs ) # signals from hidden layer
        
        # TODO: Output layer - Replace these values with the appropriate calculations.
        final_inputs = np.dot(hidden_outputs,self.weights_hidden_to_output) # signals into final output layer
        final_outputs = final_inputs # signals from final output layer 
        
        return final_outputs
In [10]:
def MSE(y, Y):
    return np.mean((y-Y)**2)

单元测试

运行这些单元测试,检查你的网络实现是否正确。这样可以帮助你确保网络已正确实现,然后再开始训练网络。这些测试必须成功才能通过此项目。

In [11]:
import unittest

inputs = np.array([[0.5, -0.2, 0.1]])
targets = np.array([[0.4]])
test_w_i_h = np.array([[0.1, -0.2],
                       [0.4, 0.5],
                       [-0.3, 0.2]])
test_w_h_o = np.array([[0.3],
                       [-0.1]])

class TestMethods(unittest.TestCase):
    
    ##########
    # Unit tests for data loading
    ##########
    
    def test_data_path(self):
        # Test that file path to dataset has been unaltered
        self.assertTrue(data_path.lower() == 'bike-sharing-dataset/hour.csv')
        
    def test_data_loaded(self):
        # Test that data frame loaded
        self.assertTrue(isinstance(rides, pd.DataFrame))
    
    ##########
    # Unit tests for network functionality
    ##########

    def test_activation(self):
        network = NeuralNetwork(3, 2, 1, 0.5)
        # Test that the activation function is a sigmoid
        self.assertTrue(np.all(network.activation_function(0.5) == 1/(1+np.exp(-0.5))))

    def test_train(self):
        # Test that weights are updated correctly on training
        network = NeuralNetwork(3, 2, 1, 0.5)
        network.weights_input_to_hidden = test_w_i_h.copy()
        network.weights_hidden_to_output = test_w_h_o.copy()
        
        network.train(inputs, targets)
        self.assertTrue(np.allclose(network.weights_hidden_to_output, 
                                    np.array([[ 0.37275328], 
                                              [-0.03172939]])))
        self.assertTrue(np.allclose(network.weights_input_to_hidden,
                                    np.array([[ 0.10562014, -0.20185996], 
                                              [0.39775194, 0.50074398], 
                                              [-0.29887597, 0.19962801]])))

    def test_run(self):
        # Test correctness of run method
        network = NeuralNetwork(3, 2, 1, 0.5)
        network.weights_input_to_hidden = test_w_i_h.copy()
        network.weights_hidden_to_output = test_w_h_o.copy()

        self.assertTrue(np.allclose(network.run(inputs), 0.09998924))

suite = unittest.TestLoader().loadTestsFromModule(TestMethods())
unittest.TextTestRunner().run(suite)
.....
self.weights_hidden_to_output  (2, 1)
self.weights_hidden_to_output  (2, 1)
self.weights_hidden_to_output  (2, 1)
X [ 0.5 -0.2  0.1]
hidden_inputs [-0.06 -0.18]
hidden_outputs [ 0.4850045   0.45512111]
error [ 0.30001076]
hidden_error [ 0.09000323 -0.03000108]
hidden_outputs*(1-hidden_outputs) [ 0.24977513  0.24798589]
hidden_error_term [ 0.02248057 -0.00743984]
X= [ 0.5 -0.2  0.1]
----------------------------------------------------------------------
Ran 5 tests in 0.023s

OK
Out[11]:
<unittest.runner.TextTestResult run=5 errors=0 failures=0>

训练网络

现在你将设置网络的超参数。策略是设置的超参数使训练集上的错误很小但是数据不会过拟合。如果网络训练时间太长,或者有太多的隐藏节点,可能就会过于针对特定训练集,无法泛化到验证数据集。即当训练集的损失降低时,验证集的损失将开始增大。

你还将采用随机梯度下降 (SGD) 方法训练网络。对于每次训练,都获取随机样本数据,而不是整个数据集。与普通梯度下降相比,训练次数要更多,但是每次时间更短。这样的话,网络训练效率更高。稍后你将详细了解 SGD。

选择迭代次数

也就是训练网络时从训练数据中抽样的批次数量。迭代次数越多,模型就与数据越拟合。但是,如果迭代次数太多,模型就无法很好地泛化到其他数据,这叫做过拟合。你需要选择一个使训练损失很低并且验证损失保持中等水平的数字。当你开始过拟合时,你会发现训练损失继续下降,但是验证损失开始上升。

选择学习速率

速率可以调整权重更新幅度。如果速率太大,权重就会太大,导致网络无法与数据相拟合。建议从 0.1 开始。如果网络在与数据拟合时遇到问题,尝试降低学习速率。注意,学习速率越低,权重更新的步长就越小,神经网络收敛的时间就越长。

选择隐藏节点数量

隐藏节点越多,模型的预测结果就越准确。尝试不同的隐藏节点的数量,看看对性能有何影响。你可以查看损失字典,寻找网络性能指标。如果隐藏单元的数量太少,那么模型就没有足够的空间进行学习,如果太多,则学习方向就有太多的选择。选择隐藏单元数量的技巧在于找到合适的平衡点。

In [21]:
import sys

### Set the hyperparameters here ###
iterations = 100
learning_rate = 0.5
hidden_nodes = 5
output_nodes = 1

N_i = train_features.shape[1]
network = NeuralNetwork(N_i, hidden_nodes, output_nodes, learning_rate)

losses = {'train':[], 'validation':[]}
for ii in range(iterations):
    # Go through a random batch of 128 records from the training data set
    batch = np.random.choice(train_features.index, size=128)
    X, y = train_features.ix[batch].values, train_targets.ix[batch]['cnt']
                             
    network.train(X, y)
    
    # Printing out the training progress
    train_loss = MSE(network.run(train_features).T, train_targets['cnt'].values)
    val_loss = MSE(network.run(val_features).T, val_targets['cnt'].values)
    sys.stdout.write("\rProgress: {:2.1f}".format(100 * ii/float(iterations)) \
                     + "% ... Training loss: " + str(train_loss)[:5] \
                     + " ... Validation loss: " + str(val_loss)[:5])
    sys.stdout.flush()
    
    losses['train'].append(train_loss)
    losses['validation'].append(val_loss)
self.weights_hidden_to_output  (5, 1)
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hidden_error [-0.29882284  0.28680936 -0.23920925  0.6639161  -0.33344882]
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hidden_error [-0.96626375  0.92741736 -0.7734992   2.14681738 -1.0782292 ]
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hidden_error [-0.07212577  0.06922613 -0.05773706  0.160247   -0.08048332]
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hidden_inputs [-0.99344206  0.77422689  0.22006397 -0.85496036  0.63882823]
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error [-0.88919339]
hidden_error [ 0.23483021 -0.24522832  0.20010517 -0.56570279  0.29402602]
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hidden_inputs [-1.1568776   0.66610209  0.32394029 -0.67052857  0.4286288 ]
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hidden_error [ 0.22289617 -0.23276585  0.18993584 -0.53695384  0.27908365]
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hidden_inputs [ 0.16264186  0.6425605   0.25334958  0.77321842 -0.3887866 ]
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hidden_inputs [ 0.23427656  0.03851742 -0.26630396 -0.1387168  -0.1114735 ]
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hidden_error [ 0.1075786  -0.11234211  0.09167063 -0.25915539  0.13469693]
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hidden_error [ 0.16168017 -0.16883925  0.13777204 -0.38948534  0.20243638]
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hidden_error [-0.3754713   0.3920969  -0.31994923  0.90450525 -0.4701198 ]
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hidden_error [ 0.20955368 -0.21883256  0.17856635 -0.50481196  0.2623778 ]
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hidden_error [-0.18912981  0.19750434 -0.16116262  0.45561114 -0.2368055 ]
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hidden_error [ 0.0315747  -0.03297281  0.02690566 -0.07606303  0.03953403]
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hidden_error [ 0.18396653 -0.17475179  0.17639263 -0.44195993  0.26279967]
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hidden_error [ 0.11140123 -0.10582123  0.10681485 -0.26762956  0.15913877]
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hidden_error [ 0.15760061 -0.14970652  0.1511122  -0.37861863  0.22513545]
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hidden_error [-0.126523    0.09071101 -0.13321178  0.26238288 -0.19068132]
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hidden_inputs [ 0.06888653 -0.08804175  0.18270088 -0.35668191  0.47202267]
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hidden_error [ 0.20002961 -0.14341177  0.2106044  -0.41482059  0.30146226]
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hidden_error [-0.12877255  0.09232382 -0.13558025  0.26704798 -0.19407158]
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hidden_error [-0.14827254  0.10630439 -0.15611113  0.30748698 -0.22345978]
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hidden_error [-0.8353311   0.59889288 -0.87949179  1.73230619 -1.2589176 ]
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hidden_inputs [-0.54394165  0.52527298 -0.44610926  1.02641302 -0.57031146]
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hidden_error [ 0.13970151 -0.15828739  0.15181546 -0.39860907  0.24384646]
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hidden_inputs [-1.27680614  0.46243478  0.24598569  0.51006635  0.18815578]
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error [-0.97378989]
hidden_error [ 0.2056551  -0.28504881  0.22955893 -0.69722817  0.39907796]
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hidden_inputs [-0.78716372  0.36920502 -0.20984544  0.45924486 -0.68349548]
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hidden_error [-0.3115884   0.43187796 -0.34780515  1.05637164 -0.60464373]
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hidden_error_term [-0.06697528  0.1043721  -0.08600104  0.25064346 -0.13479546]
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hidden_error [-0.0983914   0.13637567 -0.1098277   0.33357431 -0.19093055]
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hidden_inputs [ 0.38157637 -0.35361255  0.19195462 -0.99412226  1.04650268]
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hidden_error [ 0.15512918 -0.21501722  0.17316025 -0.52593121  0.30103137]
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hidden_error_term [ 0.03740418 -0.05210833  0.04289373 -0.1036849   0.05790359]
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hidden_error [-0.07427119  0.10294379 -0.08290393  0.25180007 -0.14412478]
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hidden_error [-0.25822629  0.35791526 -0.28824062  0.87545919 -0.50109345]
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hidden_error [-0.25383791  0.35183273 -0.28334217  0.86058136 -0.49257771]
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error [-0.07312145]
hidden_error [ 0.01721651 -0.01900741  0.0200245  -0.05106275  0.03406457]
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hidden_error_term [ 0.00421255 -0.00426596  0.00500499 -0.01095085  0.00811475]
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hidden_inputs [-0.02319069  0.3849375   0.24929539  0.59142826 -0.31862302]
hidden_outputs [ 0.49420259  0.59506341  0.56200306  0.64369279  0.42101137]
error [ 2.30193963]
hidden_error [-0.54199374  0.59837307 -0.63039214  1.60750871 -1.07238842]
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hidden_error_term [-0.13548022  0.14418574 -0.15517457  0.36868595 -0.26140625]
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hidden_inputs [-0.53662984  0.58049945 -0.24381788  0.07144072 -0.06446982]
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hidden_error [-0.55190756  0.60931814 -0.64192289  1.63691229 -1.0920039 ]
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hidden_error [-0.18228325  0.25250011 -0.22187667  0.6495853  -0.41356097]
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hidden_inputs [-0.26805204 -0.30941191 -0.03647932 -0.75455423  0.59400308]
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hidden_error [ 0.05004919 -0.06932851  0.06092028 -0.17835548  0.1135507 ]
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hidden_error [-0.10238363  0.14182256 -0.1246222   0.36485471 -0.23228615]
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hidden_error [-0.1946502   0.2696309  -0.23692982  0.69365621 -0.44161888]
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hidden_error [-0.38687848  0.53590692 -0.47091165  1.37868164 -0.87774294]
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hidden_error [ 0.2141049  -0.29657969  0.26061024 -0.76298506  0.48575735]
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hidden_error [ 0.09364405 -0.12971643  0.11398431 -0.3337103   0.21245794]
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hidden_error [ 0.03622835 -0.0336613   0.04991704 -0.10486574  0.08631742]
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hidden_error [-0.52903422  0.49154819 -0.72892698  1.53133006 -1.26047318]
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hidden_error [-0.01818843  0.02014538 -0.02705274  0.06093922 -0.04868649]
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hidden_error [-0.00129259  0.00143166 -0.00192254  0.00433074 -0.00345998]
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hidden_error [ 0.2511887  -0.27821483  0.37360785 -0.84159209  0.67237767]
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hidden_inputs [-0.41326127  0.6249659  -0.25952007  0.98073715 -0.39395652]
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error [ 0.28365555]
hidden_error [-0.06798294  0.06612946 -0.10005297  0.2127434  -0.17947871]
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hidden_inputs [-0.36357229  0.17785357  0.44360912  0.04902758  0.83344745]
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error [ 1.91101167]
hidden_error [-0.45800689  0.44551981 -0.67406543  1.4332705  -1.20916342]
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hidden_error_term [-0.1107997   0.11050378 -0.16049034  0.35810239 -0.2553247 ]
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hidden_inputs [-0.68504753  0.61662506  0.08112922  0.71908549 -0.58497235]
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hidden_error [ 0.049525   -0.04817475  0.07288774 -0.15498177  0.13074872]
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hidden_inputs [ 0.16022652  0.9136889   0.13499218  0.96982399 -0.5653445 ]
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hidden_error [-0.39099211  0.38033211 -0.57543733  1.22355681 -1.0322407 ]
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hidden_error [ 0.05205967 -0.05064032  0.07661812 -0.1629137   0.13744041]
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hidden_error [ 0.1865086  -0.18142363  0.2744915  -0.58365338  0.49239297]
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hidden_inputs [ 0.06747294  0.71665217 -0.43461347  1.40958451 -1.14353079]
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hidden_error [-0.81014186  0.78805419 -1.19231531  2.53522918 -2.13881916]
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hidden_inputs [ 0.21423629  0.06392987  0.85130542 -0.71773051  0.59976173]
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hidden_error [ 0.11746066 -0.11425822  0.17287114 -0.36757723  0.31010262]
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hidden_inputs [-0.78982555  0.71664036  0.03230675 -0.08959974 -0.14356114]
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hidden_inputs [-0.18077836  1.06831923 -0.195074    1.72034701 -0.85451956]
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hidden_error [-0.06706052  0.11462475 -0.10860534  0.30788938 -0.22662537]
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hidden_error [-0.0489264   0.08362859 -0.07923691  0.22463172 -0.16534266]
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hidden_error [ 0.06319522 -0.1080179   0.10234544 -0.29014297  0.21356293]
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error [-0.12973197]
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hidden_error_term [ 0.00665997 -0.00980025  0.01131426 -0.02451945  0.02026666]
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hidden_error [-0.27000038  0.4042935  -0.45606334  1.15239428 -0.9219782 ]
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hidden_error [-0.11647574  0.17440859 -0.19674164  0.49713256 -0.39773313]
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hidden_inputs [ 0.4626257  -0.00292838  0.09254727 -0.59486146  0.27608627]
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hidden_error [-0.08435889  0.14972508 -0.15089062  0.40616231 -0.31512626]
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hidden_error [-0.13285005  0.23579002 -0.23762553  0.63963243 -0.49626706]
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hidden_error_term [-0.0293456   0.05339723 -0.05546524  0.13634836 -0.09096991]
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hidden_inputs [ 0.05675602  0.7199729  -0.66602793  1.47024415 -1.38474583]
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hidden_error [-0.46058299  0.81746958 -0.82383318  2.21756653 -1.72052755]
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hidden_inputs [ 0.1928041   0.55492088 -0.41924058  0.98279814 -0.99513458]
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hidden_error [-0.61877269  1.09823389 -1.1067831   2.97920166 -2.31145197]
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hidden_error [-0.05199402  0.09228201 -0.09300038  0.25033532 -0.19422588]
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hidden_error [-0.00117044  0.00207737 -0.00209354  0.00563531 -0.00437223]
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hidden_error [-0.02385714  0.04691556 -0.04401565  0.12470619 -0.095064  ]
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hidden_inputs [-1.09166654  0.26676368  0.09626783 -0.46117552  0.40039824]
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hidden_error [ 0.1177663  -0.23158987  0.217275   -0.61558874  0.46926562]
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hidden_error [-0.01384515  0.0228634  -0.02536137  0.06464877 -0.05256203]
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hidden_inputs [ 0.06194689  0.60477952 -0.54353673  1.27600074 -0.49519328]
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hidden_error [ 0.17073966 -0.28195355  0.31275877 -0.79725445  0.64819974]
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hidden_error [ 0.0825881  -0.13638313  0.15128386 -0.3856382   0.31353927]
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hidden_error [ 0.02847795 -0.0470275   0.05216555 -0.13297538  0.1081143 ]
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hidden_error [ 0.12361989 -0.20414159  0.22644536 -0.57723265  0.46931322]
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hidden_error [ 0.08626174 -0.14244965  0.15801318 -0.40279194  0.32748595]
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hidden_error [-0.13629157  0.22506716 -0.24965719  0.63640199 -0.51742026]
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hidden_error [-0.08888031  0.1459423  -0.1674936   0.41472875 -0.34615396]
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hidden_inputs [ 0.36226285 -0.65132216 -0.1208377  -1.93967323  0.49077022]
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hidden_error [ 0.09443974 -0.1853386   0.18929367 -0.49608729  0.4037975 ]
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hidden_error_term [ 0.02262387 -0.04610023  0.04706429 -0.11289611  0.09878324]
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hidden_error [ 0.20394508 -0.40024355  0.40878463 -1.07131347  0.87201127]
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hidden_error [-0.0711897   0.10315932 -0.13337337  0.3007867  -0.27080467]
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hidden_error [-0.02849283  0.04128828 -0.0533811   0.12038628 -0.10838633]
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hidden_error [ 0.06400047 -0.09274157  0.1199044  -0.27041117  0.24345693]
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hidden_error [-0.12459768  0.20768181 -0.24780277  0.58066355 -0.51418654]
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hidden_inputs [-0.42821537  0.04325159  0.01850283  0.16495711  0.62966017]
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error [ 0.34732044]
hidden_error [-0.0780652   0.11854913 -0.15264496  0.34065214 -0.31124254]
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hidden_error_term [-0.01864828  0.02962343 -0.03815797  0.08458631 -0.07058061]
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hidden_inputs [-0.79679421  0.03086331  0.45969093 -0.58737771  0.47929362]
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hidden_error [ 0.14564254 -0.22117149  0.28478246 -0.63553854  0.58067043]
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hidden_error [ 0.04951115 -0.07518719  0.09681173 -0.21605117  0.19739877]
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hidden_error [ 0.21943193 -0.33322741  0.4290667  -0.95753238  0.8748655 ]
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hidden_error [ 0.10842832 -0.21045256  0.22288855 -0.56078644  0.47678662]
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hidden_error_term [ 0.02274992 -0.05258132  0.05396102 -0.13621768  0.11750791]
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hidden_error [-0.20262531  0.39328301 -0.41652276  1.04796911 -0.89099452]
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hidden_error [ 0.1109005  -0.21525091  0.22797045 -0.57357246  0.48765743]
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hidden_inputs [-0.28966941  0.73335617 -0.23335643  0.8671908  -0.59944187]
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hidden_error [-0.36029306  0.69930621 -0.74062938  1.86341969 -1.58429931]
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hidden_inputs [-0.56521556  1.00673174 -0.32114601  1.49317158 -1.22984554]
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hidden_error [ 0.01498741 -0.02908961  0.03080857 -0.0775142   0.0659034 ]
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hidden_inputs [ 0.20007563 -0.07842079  0.49923538 -1.50246528  1.03743525]
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error [-0.34253368]
hidden_error [ 0.06722896 -0.13707786  0.14050173 -0.359218    0.30425387]
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hidden_inputs [-0.22141382  0.60523713  0.06855049  0.83246382 -0.49636981]
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hidden_error [ 0.24313573 -0.49574655  0.50812909 -1.29912358  1.10034402]
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hidden_error_term [ 0.06004501 -0.11324538  0.12688315 -0.27442684  0.25881414]
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hidden_inputs [ 0.60789992 -0.62830611  0.34057662 -1.41867146  0.16492954]
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hidden_error [-0.14599723  0.29768404 -0.30511946  0.78009288 -0.66073048]
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hidden_error [-0.11991491  0.24450296 -0.25061005  0.64072975 -0.54269137]
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hidden_error [ 0.1148835  -0.23424406  0.24009491 -0.61384589  0.51992102]
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hidden_error [-0.11353775  0.23150011 -0.23728242  0.60665527 -0.51383064]
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hidden_error [ 0.06832588 -0.13931444  0.14279418 -0.36507905  0.30921812]
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hidden_inputs [ 0.46197119  0.01392763 -0.10489713  0.46196267 -0.39111041]
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hidden_error [-0.18869422  0.38474193 -0.39435185  1.00823156 -0.85396153]
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hidden_error [-0.28725119  0.58569667 -0.60032595  1.53484146 -1.29999459]
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hidden_error [ 0.21728313 -0.44303388  0.45409979 -1.16098793  0.98334458]
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hidden_error [ 0.02606606 -0.05001561  0.05362858 -0.1330627   0.1158677 ]
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hidden_inputs [-0.11947998 -0.21947838  0.15598059  0.5078775  -0.5103115 ]
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hidden_error [-0.51224292  0.98289282 -1.05389381  2.61491085 -2.27699942]
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hidden_error [-0.24350868  0.45309661 -0.48843316  1.20996687 -1.05915273]
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hidden_error [-0.12013451  0.22353429 -0.2409675   0.59693469 -0.52253084]
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hidden_error [-0.12931047  0.24060799 -0.25937277  0.64252898 -0.56244211]
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hidden_inputs [ 0.0455151   0.10162775  0.03360438  0.57827477 -0.31918975]
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error [ 2.46780781]
hidden_error [-0.46352104  1.05662627 -0.98289043  2.67796712 -2.22568153]
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hidden_inputs [-0.69511654 -0.27280467  1.13501083 -2.06287483  1.65177145]
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hidden_error [-0.04769704  0.10872849 -0.10114096  0.275567   -0.2290261 ]
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hidden_error_term [-0.01059238  0.02668259 -0.01861732  0.0275687  -0.03091638]
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hidden_inputs [-0.41760326  0.24451627  0.06667153  0.21867214 -0.86426045]
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hidden_error [ 0.0691748  -0.15768843  0.14668427 -0.39965355  0.33215551]
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hidden_error_term [ 0.01656111 -0.03883869  0.03663035 -0.09872844  0.06927681]
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hidden_inputs [-0.73454683  0.96121291 -0.81537358  2.42050296 -1.86530053]
hidden_outputs [ 0.32419775  0.72336458  0.3067466   0.91837745  0.13408643]
error [-0.29919094]
hidden_error [ 0.05619615 -0.12810277  0.11916321 -0.32467014  0.26983615]
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hidden_outputs*(1-hidden_outputs) [ 0.2499979   0.21518486  0.14902597  0.09454858  0.13857741]
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hidden_error [-0.03041391  0.06933049 -0.06449231  0.1757147  -0.146038  ]
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hidden_error [-0.21454142  0.48906109 -0.45493235  1.2395012  -1.03016011]
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hidden_inputs [-0.18085749  0.40600148 -0.50622981 -0.02994573 -0.28504842]
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hidden_error [ 0.12029664 -0.32231845  0.26820097 -0.79156068  0.63215441]
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hidden_error_term [ 0.02733359 -0.08030683  0.05949113 -0.1847822   0.13889857]
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hidden_inputs [ 0.25012281  0.55580069 -0.20987229 -0.18365274 -0.62622016]
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hidden_error [-0.22240993  0.59591708 -0.49586221  1.46347357 -1.16875598]
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hidden_inputs [-0.17038736  0.25950467 -0.09931019 -0.06830326 -0.48225657]
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hidden_error [ 0.01235851 -0.03311293  0.02755325 -0.08131987  0.06494349]
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hidden_error [-0.24903493  0.66725515 -0.55522257  1.63866803 -1.30866939]
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hidden_error [-0.00626013  0.01677316 -0.01395694  0.04119211 -0.03289675]
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hidden_error [-0.30540236  0.83874078 -0.69218888  2.08733966 -1.66418161]
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hidden_inputs [-1.07928527  0.37099918 -0.04578127 -0.22993438  0.51409748]
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hidden_error [ 0.17067939 -0.46874481  0.38684174 -1.16654591  0.93005671]
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hidden_error_term [ 0.03231087 -0.11324454  0.09665978 -0.2878155   0.21780327]
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hidden_inputs [-0.36694803  0.87117176 -0.13202696  0.83167041 -0.64619842]
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hidden_error [ 0.07666467 -0.1744446   0.16431339 -0.45132703  0.38053376]
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hidden_inputs [ 0.13369379  0.07828803 -0.81570605 -0.39082882 -0.0193573 ]
hidden_outputs [ 0.53337375  0.51956202  0.3066759   0.40351779  0.49516083]
error [-0.26725888]
hidden_error [ 0.04497701 -0.1268598   0.10424342 -0.31533955  0.25323024]
hidden_outputs*(1-hidden_outputs) [ 0.24888619  0.24961733  0.21262579  0.24069118  0.24997658]
hidden_error_term [ 0.01119416 -0.03166641  0.02216484 -0.07589945  0.06330163]
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hidden_inputs [-0.72924083 -0.92031162  0.51283346 -2.46158513  1.97134311]
hidden_outputs [ 0.32536134  0.2848944   0.62547047  0.07859547  0.8777553 ]
error [-0.11452232]
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hidden_error [-0.43696383  0.8227268  -0.90574513  2.24413811 -2.03897323]
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hidden_inputs [-0.64596115 -0.3328194   0.28598519 -1.08725271  0.91795751]
hidden_outputs [ 0.34390026  0.41755478  0.57101296  0.25213596  0.71462575]
error [ 1.3114895]
hidden_error [-0.29209895  0.54997146 -0.60546706  1.50014795 -1.36300057]
hidden_outputs*(1-hidden_outputs) [ 0.22563287  0.24320279  0.24495716  0.18856342  0.20393579]
hidden_error_term [-0.06590713  0.13375459 -0.14831349  0.28287303 -0.27796459]
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hidden_inputs [ 0.03393889  0.40552444  0.48835948  0.72947609 -0.40434834]
hidden_outputs [ 0.50848391  0.60001424  0.61971989  0.67469029  0.40026805]
error [-1.31071977]
hidden_error [ 0.24924736 -0.61442651  0.57016007 -1.56555352  1.34442294]
hidden_outputs*(1-hidden_outputs) [ 0.24992802  0.23999715  0.23566715  0.2194833   0.24005354]
hidden_error_term [ 0.0622939  -0.14746061  0.134368   -0.34361286  0.32273348]
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hidden_inputs [-1.09903038  0.68909022  0.29255411  0.16564805 -0.00619484]
hidden_outputs [ 0.24992162  0.66576451  0.57262131  0.54131758  0.4984513 ]
error [-0.73770722]
hidden_error [ 0.14028291 -0.34581524  0.32090093 -0.88113429  0.75667624]
hidden_outputs*(1-hidden_outputs) [ 0.1874608   0.22252213  0.24472615  0.24829286  0.2499976 ]
hidden_error_term [ 0.02629755 -0.07695154  0.07853285 -0.21877935  0.18916724]
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hidden_inputs [-0.12351132  0.57608633 -0.23433132  0.31222355 -0.19318317]
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error [-0.93664901]
hidden_error [ 0.17811381 -0.43907325  0.40744016 -1.1187549   0.96073352]
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hidden_inputs [-0.47095587 -0.9016846   0.92953751 -1.92593921  2.3555577 ]
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error [ 0.66264687]
hidden_error [-0.12600938  0.31062917 -0.28824986  0.7914805  -0.67968582]
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hidden_error_term [-0.02981815  0.063789   -0.05849139  0.08787072 -0.05377751]
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hidden_inputs [-0.11832937  0.10351574 -0.35932799 -0.53175956  0.26814189]
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hidden_error [ 0.15753934 -0.38835454  0.36037549 -0.98952407  0.84975622]
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hidden_error_term [ 0.03924729 -0.09682901  0.08724717 -0.23068547  0.20866576]
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hidden_inputs [ 0.18026746 -0.69486428  0.137713   -0.64893594  0.41580435]
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hidden_error [ 0.10177838 -0.25089667  0.23282079 -0.63928259  0.5489855 ]
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hidden_error_term [ 0.025239   -0.05572288  0.0579301  -0.14410898  0.13148098]
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hidden_inputs [ 0.06807948  1.01986932 -0.34061373  2.06918279 -1.11133907]
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hidden_error [-0.17443252  0.42999839 -0.3990191   1.09563224 -0.94087688]
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hidden_inputs [-0.58063149 -1.25936249  0.93737017 -2.12619233  2.584413  ]
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error [ 0.08116025]
hidden_error [-0.01543349  0.03804551 -0.03530452  0.09693965 -0.08324716]
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hidden_inputs [-0.56124635  0.36050548 -0.47485845  0.62511362 -0.36344236]
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hidden_error [ 0.26061515 -0.64244955  0.59616418 -1.63695598  1.40573997]
hidden_outputs*(1-hidden_outputs) [ 0.23130193  0.24205     0.23642005  0.22708389  0.24192276]
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hidden_error [-0.12713834  0.31341222 -0.29083239  0.79857167 -0.68577538]
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hidden_error [-0.03667662  0.09041253 -0.08389875  0.23037036 -0.19783112]
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hidden_error [-0.06859603  0.16909796 -0.15691528  0.43086017 -0.37000223]
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hidden_error [ 0.06588701 -0.16241986  0.1507183  -0.41384443  0.35538992]
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hidden_error [-0.16786051  0.30503931 -0.35607177  0.84565819 -0.79495518]
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hidden_error [-0.03845219  0.06987605 -0.08156617  0.19371684 -0.18210218]
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hidden_error [ 0.18385298 -0.33410113  0.38999558 -0.92622606  0.87069245]
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hidden_inputs [-0.5597519   1.08551846 -0.28117356  1.70792107 -1.14950646]
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hidden_error [-0.31994975  0.58141878 -0.67868898  1.61186294 -1.51522069]
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hidden_error_term [-0.07403521  0.10972855 -0.16636243  0.20936762 -0.27683214]
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hidden_inputs [-0.23281673 -0.08893416 -0.02568313 -0.39754131  0.14561622]
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error [ 1.73120904]
hidden_error [-0.3905006   0.70962512 -0.82834398  1.96728841 -1.84933597]
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hidden_error [ 0.12724124 -0.30035072  0.28808515 -0.77659441  0.67728847]
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hidden_error [ 0.08951017 -0.2112872   0.20265876 -0.54630952  0.47645094]
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hidden_error [-0.12636868  0.29829105 -0.28610959  0.77126888 -0.67264394]
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hidden_error [ 0.07390801 -0.17445856  0.16733411 -0.45108446  0.39340265]
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hidden_error [-0.42636884  1.00643617 -0.96533583  2.60226676 -2.2695055 ]
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hidden_error_term [ 0.00215081 -0.00765364  0.0072221  -0.01578847  0.01545451]
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hidden_error [-0.24866919  0.57118218 -0.5543493   1.47526414 -1.30123982]
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hidden_error_term [-0.06203999  0.12908213 -0.1373206   0.32720234 -0.29826942]
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hidden_inputs [-0.54559947  0.97926031 -0.83648746  1.22411743 -1.10410309]
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hidden_error [-0.31078393  0.713857   -0.69281945  1.84376836 -1.62627474]
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hidden_inputs [-0.61807083  0.36134519 -0.20845855  0.55691385 -0.1877523 ]
hidden_outputs [ 0.35022034  0.58936603  0.44807327  0.63573816  0.45319932]
error [-1.25285592]
hidden_error [ 0.25464539 -0.58490923  0.56767181 -1.51071872  1.33251213]
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hidden_error_term [ 0.05794865 -0.14155605  0.14038729 -0.34984492  0.33020943]
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hidden_inputs [-0.33935792 -0.07898038  0.48580061  0.5004675   0.15648262]
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hidden_error [-0.02913443  0.05895739 -0.06375816  0.15790693 -0.14592917]
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hidden_error [-0.07204777  0.14579825 -0.15767029  0.39049481 -0.3608745 ]
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hidden_error [-0.0264661   0.05355767 -0.05791876  0.14344475 -0.132564  ]
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hidden_error [-0.18824328  0.38093532 -0.41195406  1.02026782 -0.94287715]
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hidden_error_term [-0.03929915  0.08768083 -0.10291753  0.18960731 -0.21839621]
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hidden_error [ 0.10980604 -0.22220712  0.24030097 -0.59514245  0.54999894]
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hidden_inputs [-0.21473341  0.58304484 -0.49642821  0.12557575 -0.07386898]
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hidden_error [ 0.11839572 -0.2395895   0.25909876 -0.64169806  0.59302316]
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hidden_inputs [-1.44786934 -0.43316762  0.84837399 -1.69009375  1.75359721]
hidden_outputs [ 0.19032969  0.39337019  0.70022594  0.15576351  0.85240594]
error [-0.15985911]
hidden_error [ 0.02992401 -0.07525771  0.07063018 -0.19392326  0.17033865]
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hidden_error_term [ 0.00461142 -0.01795875  0.01482595 -0.02550115  0.02143032]
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hidden_inputs [-1.79469605  0.47881404  0.53212554 -1.21758642  0.9053375 ]
hidden_outputs [ 0.14249794  0.61746779  0.62997872  0.22836147  0.71204512]
error [-0.3941269]
hidden_error [ 0.07377657 -0.18554518  0.17413618 -0.47811085  0.41996385]
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hidden_error_term [ 0.00901493 -0.04382602  0.04059211 -0.08424911  0.08610807]
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hidden_inputs [-0.793405    0.12467274  0.66838575 -0.36564985  0.68048835]
hidden_outputs [ 0.31143802  0.53112788  0.66114161  0.40959259  0.66384768]
error [ 0.02162899]
hidden_error [-0.00404873  0.01018239 -0.00955629  0.02623788 -0.02304687]
hidden_outputs*(1-hidden_outputs) [ 0.21444438  0.24903106  0.22403338  0.2418265   0.22315394]
hidden_error_term [-0.00086823  0.00253573 -0.00214093  0.00634501 -0.005143  ]
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hidden_inputs [ 0.00925838  0.59472613  0.12306254  0.17867313  0.41818221]
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hidden_error [ 0.10003502 -0.23867318  0.23202515 -0.62270965  0.55839983]
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hidden_error [ 0.04088204 -0.09754031  0.09482342 -0.25448731  0.22820534]
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hidden_error [-0.0883098   0.21069802 -0.20482921  0.54972113 -0.49294913]
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hidden_inputs [-0.72671559  0.65454817 -0.71804661  1.41848887 -1.89550542]
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hidden_error [ 0.09724205 -0.29287007  0.24641749 -0.72565068  0.62507865]
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hidden_inputs [ 0.03324917  0.05629985  0.30568774 -1.11472513  0.6600843 ]
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hidden_error [ 0.04510544 -0.11880655  0.10784567 -0.29892228  0.26821717]
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hidden_inputs [-0.05472479 -0.21087818  0.67438522 -0.74929767  0.91820405]
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error [ 1.61020642]
hidden_error [-0.30196676  0.79537263 -0.721993    2.00119103 -1.79562991]
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hidden_error [-0.1392515   0.36678485 -0.33294595  0.92284612 -0.82805193]
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hidden_error [-0.18290512  0.48176736 -0.43732038  1.21214696 -1.08763596]
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hidden_error [ 0.11433708 -0.3011609   0.27337634 -0.7577335   0.67989958]
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hidden_inputs [-0.3055331   0.37175132  0.17928605 -0.46895004  0.26990751]
hidden_outputs [ 0.42420543  0.59188209  0.54470184  0.38486478  0.5670702 ]
error [-0.69557439]
hidden_error [ 0.13518547 -0.33257957  0.325967   -0.85698678  0.79377202]
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hidden_error_term [ 0.03301975 -0.08033715  0.08084038 -0.20288638  0.19487229]
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hidden_inputs [-0.66320554  1.40830808 -1.19313698  2.29433257 -1.48278087]
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hidden_error [-0.08561356  0.21062412 -0.20643635  0.54273354 -0.50269936]
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hidden_error_term [-0.01921223  0.0332551  -0.03685918  0.04515764 -0.07579695]
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hidden_inputs [-0.63207955  0.08227131 -0.15673422 -0.84623544  0.09438784]
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hidden_error [ 0.00526453 -0.01295166  0.01269414 -0.03337367  0.03091189]
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hidden_inputs [-0.2629228   0.92195493  0.00908929  0.56883898 -0.48998707]
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hidden_error [ 0.12380632 -0.3045849   0.29852894 -0.78485046  0.72695677]
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hidden_inputs [-0.79569231 -0.13462383  0.84819286 -1.44492045  1.13207664]
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hidden_error [ 0.04771737 -0.11739296  0.11505888 -0.30249668  0.28018332]
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hidden_inputs [-0.78330307  0.43619903 -0.07945535  0.81394393 -0.39144121]
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hidden_error [ 0.11961033 -0.29426203  0.28841132 -0.75825063  0.70231905]
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hidden_inputs [-0.45072055 -0.25661687  0.43027184 -0.16743301  1.08412671]
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hidden_error [ 0.01049142 -0.02581071  0.02529753 -0.06650871  0.06160276]
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hidden_inputs [-1.17641987 -0.48686984  0.38504189 -2.19573261  1.37107116]
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hidden_error [-0.01085469  0.02670441 -0.02617346  0.06881159 -0.06373577]
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hidden_error [ 0.16824088 -0.44928562  0.40342539 -1.14319973  1.03006181]
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hidden_error [-0.00078332  0.00200432 -0.00184902  0.00517922 -0.00473654]
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hidden_inputs [-0.64940731  0.8183157  -0.45692057  0.79634544 -0.27184918]
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hidden_error [ 0.24904588 -0.63724215  0.5878693  -1.64665583  1.50591122]
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hidden_error [-0.06748098  0.17266588 -0.15928791  0.44617464 -0.40803875]
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hidden_inputs [-0.4179501   0.80505809 -0.24575788  0.81694088 -0.61596827]
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error [ 0.04941154]
hidden_error [-0.00968274  0.02346323 -0.0224396   0.06175104 -0.05741084]
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hidden_error [ 0.04746506 -0.11501745  0.10999961 -0.30270547  0.28142966]
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hidden_inputs [ 0.36767515  0.08742904 -0.28578118  0.47861397 -0.46799995]
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hidden_error [-0.09737461  0.23595838 -0.22566429  0.62100049 -0.57735314]
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hidden_inputs [ 0.31922763  0.10138082 -0.38356772  0.35184834 -0.12517079]
hidden_outputs [ 0.57913601  0.52532352  0.40526669  0.58706572  0.4687481 ]
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hidden_error [ 0.10158553 -0.24616229  0.23542304 -0.64785539  0.60232053]
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hidden_error [ 0.04470525 -0.12147548  0.10891724 -0.31360151  0.28556219]
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hidden_error_term [ 0.00927311 -0.03020529  0.02683881 -0.07819771  0.07020281]
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hidden_inputs [-0.71192148  0.24211441 -0.41822721  1.36294298 -0.50341948]
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hidden_error [ 0.18253883 -0.49600423  0.44472689 -1.28048619  1.16599704]
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hidden_inputs [ 0.57610518  0.08325747  0.19567799 -0.82729265  0.63128458]
hidden_outputs [ 0.64017072  0.52080235  0.548764    0.30421783  0.65278068]
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hidden_error [ 0.09596024 -0.26074829  0.23379191 -0.67314867  0.61296198]
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hidden_error_term [ 0.02210465 -0.06507424  0.05789204 -0.14248493  0.13893278]
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hidden_error [ 0.15374768 -0.4177714   0.37458183 -1.07852004  0.98208882]
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hidden_error [ 0.17113293 -0.46501153  0.41693824 -1.20047534  1.09314001]
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hidden_inputs [-1.08318456  0.18173227  0.6816374  -0.52834975  1.19982652]
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hidden_error [ 0.01399601 -0.0380307   0.03409905 -0.09818017  0.08940182]
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hidden_inputs [-0.40864024  0.06028418 -0.65722846  0.23738206 -0.16554136]
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hidden_error [ 0.09974388 -0.26908926  0.24220811 -0.69398827  0.63528246]
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hidden_inputs [-0.10160323  0.48619765 -0.18744257  0.04228383  0.02397454]
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error [ 2.14394007]
hidden_error [-0.3028195   1.1360169  -0.87024992  2.84957102 -2.52090295]
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hidden_error [ 0.02434662 -0.06441306  0.06074198 -0.17267567  0.16536506]
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hidden_error [-0.09787553  0.25894605 -0.24418798  0.69417107 -0.6647818 ]
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hidden_inputs [-0.14292021 -0.4048328   0.03335607 -0.49240125  0.84585377]
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hidden_error [ 0.09543001 -0.25247603  0.2380867  -0.67682653  0.64817158]
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error [-0.64259092]
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hidden_error [-0.09197021  0.25640225 -0.23069959  0.67906251 -0.64417523]
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hidden_inputs [-0.51292241 -0.28584006 -0.01655413 -0.89581829  0.72455877]
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hidden_error [ 0.00019142 -0.00053367  0.00048017 -0.00141337  0.00134076]
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hidden_inputs [ 0.21423383  0.37120143  0.65061513  0.64077034 -0.16074713]
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error [ 0.25710052]
hidden_error [-0.04523006  0.12609615 -0.11345583  0.33395639 -0.31679916]
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hidden_inputs [-0.08131217  0.4224835  -0.10422622  0.10644306  0.10682257]
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hidden_error [ 0.01000033 -0.02787976  0.02508499 -0.07383748  0.07004403]
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error [ 0.48424858]
hidden_error [-0.08476869  0.24469375 -0.21271165  0.63905439 -0.60008659]
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hidden_inputs [ 0.38706643 -0.05041094  0.24545635 -0.08166774 -0.04824395]
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error [ 1.25892605]
hidden_error [-0.22037755  0.63614299 -0.55299746  1.66138273 -1.56007612]
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hidden_inputs [-0.21026314  0.41855976 -0.18590654  0.28866965 -0.88436656]
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hidden_error [-0.51000947  1.47219602 -1.27977622  3.84486049 -3.61041135]
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hidden_inputs [-0.64809615  0.91719933 -0.3418868   1.67348351 -0.86621546]
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error [ 3.42928903]
hidden_error [-0.60030397  1.7328406  -1.50635388  4.52557286 -4.24961573]
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hidden_error [-0.02003398  0.05783019 -0.05027164  0.15103222 -0.14182268]
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hidden_error [ 0.0522293  -0.15076538  0.13105996 -0.39374638  0.36973679]
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hidden_error [-0.20097624  0.58013908 -0.50431341  1.51512014 -1.42273223]
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error [ 0.17691857]
hidden_error [-0.02564109  0.09664285 -0.07242203  0.24028261 -0.21489811]
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hidden_error [ 0.02479271 -0.09344528  0.07002584 -0.23233251  0.2077879 ]
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hidden_error_term [ 0.00524546 -0.0233188   0.01415787 -0.02976108  0.03510014]
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hidden_inputs [-0.0059699  -0.2224077   0.27711276  0.257493    0.33273827]
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hidden_error [-0.18473244  0.69626809 -0.52176799  1.73112769 -1.54824384]
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hidden_error_term [-0.0461827   0.17193208 -0.12796949  0.42568681 -0.37654225]
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hidden_inputs [-0.91647062  0.13258284 -0.18712291 -0.82963946  0.19770466]
hidden_outputs [ 0.28567758  0.53309724  0.4533553   0.30372131  0.5492658 ]
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hidden_error [-0.03762027  0.14179314 -0.10625666  0.35253954 -0.31529573]
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hidden_error [-0.02405542  0.07461232 -0.06346852  0.19266745 -0.18094353]
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hidden_error [-0.04672618  0.15164275 -0.1238193   0.38395379 -0.35715495]
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hidden_error_term [-0.0091331   0.03596543 -0.02940576  0.07978808 -0.06111863]
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hidden_error [-0.01660527  0.05388989 -0.04400216  0.1364472  -0.12692359]
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hidden_error [-0.08112028  0.26326362 -0.21495995  0.66657365 -0.62004877]
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hidden_error [ 0.00863396 -0.0280202   0.02287905 -0.07094611  0.06599428]
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hidden_error [ 0.15427795 -0.50068575  0.40881981 -1.26771762  1.17923467]
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hidden_error [ 0.12157046 -0.39453854  0.32214852 -0.99895686  0.92923262]
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hidden_inputs [ 0.27996904  0.14255137  0.67598455 -0.17282577  0.4414358 ]
hidden_outputs [ 0.56953863  0.53557762  0.6628419   0.45690078  0.6086011 ]
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hidden_error [ 0.10917797 -0.35432061  0.28930978 -0.89712654  0.83450976]
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hidden_inputs [-0.16683223 -0.34466431  0.24472434 -0.47818153 -0.10125711]
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hidden_error [ 0.12279677 -0.39904406  0.32588378 -1.01072628  0.94121357]
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hidden_error_term [ 0.03048657 -0.09685596  0.0802632  -0.23877034  0.23470128]
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hidden_error [ 0.17134595 -0.55681094  0.45472587 -1.41032911  1.31333371]
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hidden_inputs [-0.05462583  0.50878716  0.08037499 -0.30550195  0.596384  ]
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hidden_error [ 0.01901343 -0.04671007  0.04444439 -0.12351067  0.12287815]
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hidden_error [-0.06373503  0.19304834 -0.15681596  0.48571586 -0.4594812 ]
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hidden_error [-0.17335956  0.55898289 -0.43498411  1.38167787 -1.29509951]
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hidden_error [-0.03404433  0.109773   -0.08542213  0.27133374 -0.25433149]
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hidden_error [ 0.0163227  -0.05655802  0.04185505 -0.13728581  0.12681406]
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hidden_error [-0.07356621  0.25490634 -0.18864023  0.61874558 -0.57154951]
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hidden_error [-0.12918382  0.48765667 -0.33551933  1.16004066 -1.04931627]
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hidden_error [ 0.0315878  -0.11924094  0.08204059 -0.28365107  0.25657694]
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hidden_error_term [ 0.00612365 -0.02701916  0.01942201 -0.05980475  0.0436211 ]
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hidden_inputs [ 0.11905148  0.40519744 -0.28681585 -0.21046056  0.28576722]
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hidden_error [-0.11922506  0.40384934 -0.30060266  0.97953523 -0.91106685]
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hidden_error_term [ 0.02340008 -0.08843397  0.06491315 -0.18053175  0.19616541]
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hidden_error [-0.08537514  0.26370664 -0.20907407  0.64816627 -0.61661467]
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hidden_error [ 0.04042713 -0.13903028  0.10372034 -0.33502348  0.31338409]
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hidden_inputs [-0.01965667  0.38232561 -0.00654075  0.09451269 -0.01522564]
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error [-0.61987944]
hidden_error [ 0.12086841 -0.3762743   0.30055306 -0.92398607  0.88643146]
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hidden_error [ 0.03464264 -0.10784566  0.08614286 -0.26482779  0.2540641 ]
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hidden_error [ 0.07048991 -0.28855095  0.1976273  -0.67115536  0.61339993]
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hidden_error [ 0.01235186 -0.05233223  0.03478753 -0.12027756  0.10917612]
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hidden_inputs [-0.67070293  0.52393304 -0.28123194  0.72357263 -0.4395041 ]
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hidden_error [ 0.11046154 -0.46800246  0.31110172 -1.07563138  0.97635227]
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hidden_inputs [  2.45617992e-01  -5.67507092e-04   3.09744316e-01  -2.93611797e-01
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hidden_error [ 0.11126778 -0.47141833  0.3133724  -1.08348223  0.9834785 ]
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hidden_inputs [-0.39216262 -0.09173488 -0.59081625 -0.1962242   0.18417032]
hidden_outputs [ 0.4031968   0.47708235  0.35644759  0.45110075  0.54591288]
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hidden_error [ 0.0604632  -0.25616997  0.1702874  -0.58876712  0.53442483]
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hidden_inputs [-0.6424858   0.25136647 -0.3236064   0.58145636 -0.88574105]
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hidden_inputs [-0.96061382  0.64940448 -0.19263952  0.89411814 -1.05525631]
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hidden_error [-0.04912078  0.1660203  -0.12533645  0.39735909 -0.37928713]
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hidden_error [ 0.15964131 -0.53956182  0.40734032 -1.29140706  1.23267366]
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hidden_error [-0.05818114  0.19664285 -0.14845484  0.47065221 -0.44924687]
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hidden_error [-0.02649437  0.11038053 -0.07365701  0.25574011 -0.23466993]
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hidden_error [ 0.05529125 -0.23035369  0.15371519 -0.53370534  0.48973388]
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hidden_inputs [-1.53492084  0.53760568 -0.03286334 -0.66631039  0.03796388]
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hidden_error [-0.02943932  0.09874996 -0.07304436  0.23639644 -0.22597932]
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hidden_error [-0.02119708  0.08716034 -0.05588044  0.20031989 -0.18267871]
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hidden_inputs [-0.57584657  0.54981333 -0.35046162  0.96031601 -0.92070527]
hidden_outputs [ 0.35988886  0.63409228  0.41327049  0.72318507  0.28481421]
error [ 0.61601302]
hidden_error [-0.10903851  0.44835572 -0.28745085  1.0304522  -0.93970536]
hidden_outputs*(1-hidden_outputs) [ 0.23036887  0.23201926  0.24247799  0.20018842  0.20369508]
hidden_error_term [-0.02511908  0.10402716 -0.0697005   0.2062846  -0.19141336]
X= [ 1.          0.          0.95043892 -0.97045042 -0.21168512  0.          1.
  0.          0.          1.          0.          0.          0.          0.
  0.          0.          0.          1.          0.          0.          0.
  0.          0.          0.          0.          0.          0.          0.
  0.          0.          0.          0.          0.          0.          0.
  0.          0.          0.          0.          0.          0.          0.
  0.          0.          0.          1.          0.          0.          0.
  0.          0.          0.          0.          1.          0.          0.        ]
X [ 0.          0.         -0.5036826   1.25833914 -0.69966852  0.          0.
  0.          1.          1.          0.          0.          0.          0.
  0.          0.          0.          0.          0.          0.          0.
  0.          1.          0.          0.          0.          0.          1.
  0.          0.          0.          0.          0.          0.          0.
  0.          0.          0.          0.          0.          0.          0.
  0.          0.          0.          0.          0.          0.          0.
  0.          1.          0.          0.          0.          0.          0.        ]
hidden_inputs [-0.15625487 -0.0955387   0.31879031 -1.27140464  1.10490747]
hidden_outputs [ 0.46101557  0.47613348  0.57902941  0.2190169   0.75117849]
error [-0.2211507]
hidden_error [ 0.03914518 -0.16096118  0.1031958  -0.36993573  0.33735732]
hidden_outputs*(1-hidden_outputs) [ 0.24848021  0.24943039  0.24375435  0.1710485   0.18690937]
hidden_error_term [ 0.0097268  -0.04014861  0.02515443 -0.06327695  0.06305524]
X= [ 0.          0.         -0.5036826   1.25833914 -0.69966852  0.          0.
  0.          1.          1.          0.          0.          0.          0.
  0.          0.          0.          0.          0.          0.          0.
  0.          1.          0.          0.          0.          0.          1.
  0.          0.          0.          0.          0.          0.          0.
  0.          0.          0.          0.          0.          0.          0.
  0.          0.          0.          0.          0.          0.          0.
  0.          1.          0.          0.          0.          0.          0.        ]
Progress: 99.0% ... Training loss: 0.451 ... Validation loss: 0.751
In [22]:
plt.plot(losses['train'], label='Training loss')
plt.plot(losses['validation'], label='Validation loss')
plt.legend()
_ = plt.ylim()

检查预测结果

使用测试数据看看网络对数据建模的效果如何。如果完全错了,请确保网络中的每步都正确实现。

In [23]:
fig, ax = plt.subplots(figsize=(8,4))


mean, std = scaled_features['cnt']
predictions = network.run(test_features).T*std + mean
ax.plot(predictions[0], label='Prediction')
ax.plot((test_targets['cnt']*std + mean).values, label='Data')
ax.set_xlim(right=len(predictions))
ax.legend()

dates = pd.to_datetime(rides.ix[test_data.index]['dteday'])
dates = dates.apply(lambda d: d.strftime('%b %d'))
ax.set_xticks(np.arange(len(dates))[12::24])
_ = ax.set_xticklabels(dates[12::24], rotation=45)

可选:思考下你的结果(我们不会评估这道题的答案)

请针对你的结果回答以下问题。模型对数据的预测效果如何?哪里出现问题了?为何出现问题呢?

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请将你的答案填写在下方

In [ ]:
预测在总体趋势上与实际值相同但是预测值和实际值误差相对较大
In [ ]: